1. Field of the Invention
This invention relates to the three dimensional imaging of objects using a single pulse of energy or a reduced number of pulses of energy.
2. Description of the Prior Art
A previous patent, U.S. Pat. No. 4,688,430, describes a similar machine. However in that application the reconstruction process was carried out in two geometrical steps. In the first step the image was resolved with respect to each of two angular directions originating at the transmitting transducer. In the second step the ranges along each two dimensional angular direction are resolved. This requires a complicated mathematical algorithm to be implemented in the reconstruction hardware, and in addition, mathematical approximations to the wavefield geometry may be required.
The previous patent essentially uses spherical coordinates originating at the center of the transmitting transducer. This yields a lateral resolution that is very small near the transducer but grows larger as the distance from the transducer increases. However, a large aperture formed by a sparse array is capable of producing relatively uniform resolution for ranges equal to several diameters of the array. The previous patent shows an intermediate memory called the data memory which is used to store the three dimensional reconstructed field of reflecting objects. This is an intermediate memory since it must be further processed into a tomographic image or a two dimensional view through a three dimensional field of objects. The present invention can reconstruct tomograms or two dimensional views through three dimensional fields directly from the stored time history of the receiver elements. This increases the processing speed and reduces the amount of electronics by eliminating the requirements for an intermediate memory.
The final display will most likely be in rectangular coordinates whereas the previous approach reconstructs in spherical coordinates. This results in complex electronics being required in the implementation of the machine.
The transmitted wavefield from a small transducer emitting a pulse will approximate an expanding sphere at locations several diameters away from the transducer. This must be taken into account by the reconstruction processor or image degradation will occur. The previous approach makes no explicit provision for this and it would be hard to implement in such a two step reconstruction technique. The implementation would require look up tables or computation circuits for each reconstruction point and each receiver element. This would be hard to implement in real time and would use a large amount of electronics.
U.S. Pat. No. 4,706,499 describes a device which uses a round trip time of flight algorithm which automatically takes into account the curved nature of the wavefront propagating away from the transmitter. In addition no Fraunhofer or Fresnel approximations are made since the algorithm is essentially a Huygens wavelet based approach. It requires only the computation of the distance from the transmitter to the reconstruction point and computation of the distance from the reconstruction point to each receiver element.
However, there are further improvements and modifications that can be made.
The time history memories can be eliminated by a reconstruction technique that immediately sums or combines echo samples as they are sampled into the appropriate reconstruction locations (or voxels) in the 3D memory containing the reconstructed three dimensional image.
The 3D memory can be eliminated by combining the echo samples as they are sampled into the appropriate pixels in the tomographic image and the shadowgraph image. (The shadowgraph image is the 3D memory data integrated along a specified viewing perspective vector to provide a two dimensional view through a three dimensional volume).
Multiple redundant transmitted pulses may be used to reconstruct a single image whereby the image signal to noise ratio is improved. The term "redundant" is used since only one transmitted pulse is necessary for the reconstruction of a three dimensional image.
Multiple transmitters may be used with the redundant transmitted pulses to reduce the sidelobe levels. These transmitters are to be spatially offset from one another. The receiver elements may be used as the multiple transmitters or separate transmitting elements may be used. The echoes from the multiple transmitters may be summed, or combined in another manner, in time history memories or separate images may be reconstructed from each different transmitters echoes and the resulting images combined or summed. The late may be done in the absence of time history memories.
Recording devices may be added to record the echo time histories from a number of sequential transmitted pulses. At a later time the recording then can be played back though the machine allowing image reconstruction to take place. The resulting "real time" 3D image can be viewed from various viewing perspectives and tomograms may be extracted from various positions and orientations.
If oscillations occur in the transmitted pulse, the image can be degraded. Several techniques may be used to compensate for or accommodate this.
The reconstruction technique described in U.S. Pat. No. 4,706,499 is essentially the backprojection of the echo samples over ellipsoids of revolution as will be more fully described in this application. The backprojections may be weighted as a function of the reconstruction point position to compensate for transmitter or receiver radiation patterns and other phenomena.
The sparse receiver array, by the addition of elements, may be made into a more nearly continuous array which when arranged in a circle would be a phased annulus or adjustable axicon. This sort of receiver array normally has very high sidelobes but when used with a noninterfering transmitted pulse and ellipsoidal backprojection has acceptable sidelobe levels. The addition of redundant pulsing and multiple transmitters further reduces the sidelobe level.
In forming shadowgraphs by integration (two dimensional views through three dimensional volumes), the sidelobes are integrated and the relative sidelobe level is degraded. After a three dimensional image is created of a volume containing many point reflectors, the sidelobes create a more or less continuous background level. If this background level is subtracted out (or truncated) before the shadowgraphs are created, the relative sidelobe level will not be degraded as much.
Another method of reducing sidelobes levels is to use a nonlinear form of combination in the reconstruction process (as contrasted with only using addition). For example, the echo samples may be multiplied together. The samples could be logarithmically compressed and then added together. The samples could be, first, applied to a comparator, being compared with a reference value, thus being converted to binary values, and then be combined using logic operations such as conjunction, alternation (disjunction) or more complex compound logical operations. The samples could be first compressed using the square root, then added, the results then could be decompressed by squaring.
Nonlinear combination could be useful when the three dimensional volume to be imaged contains only a few sparsely spaced objects.
The class of types of transmitted pulses that the imaging system may use can be broadened to include any type of pulse with a sharply peaked autocorrelation function that has a very small value except when the shift variable in near zero. Another measure is the integral of the sum, over time, of the pulse and a time shifted replica of itself. The amount of shift is given by the "shift variable". The result is a function of the shift variable and will be termed the "auto interference function", which is a measure of constructive and destructive interference of the pulse shape with replica of itself as a function of the shifted position of the replica. Pulses that have a peaked autointerference function that has a very small value except when the shift variable is near zero and very low amplitude oscillations are also suitable. All of these types of pulses will be termed "non interfering" or "interference free" for purposes of this application as there is little constructive and destructive interference and therefore grating lobes will not be formed when using a sparse array. A wideband white noise pulse is an example. These types of pulses also can propagate relatively uniformly through a wide solid angles. Further discussion of these types of pulses may be found in "Random Data:Analysis and Measurement Procedures" by Bendat and Piersol.
The imaging system can also function with a class of pulses which will be termed "low interference" for purposes of this application. This type of pulse has relatively low constructive and destructive interference effects as measured by the autointerference function. The function is relatively peaked around zero with relatively low amplitude oscillations as the shift variable takes on non zero values and therefore high amplitude grating lobes will not be formed when using a sparse array.
Periodic, oscillating, "interfering" pulses of a particular class may also be used for imaging if additional echo processing occurs before image reconstruction (such as echo time history convolution with a matched filter impulse response) or without additional processing if some image degradation is allowable. These pulses have an oscillating autointerference function although the oscillations may not be of equal amplitude. Even with equal amplitude oscillations, the grating lobes will be lower in amplitude than the main lobe (the reconstruction point) and the reconstructed image may be adequate for some purposes. The pulses must be of short enough duration to allow adequate lateral and range resolution. Thus, a pulse of several sinusoidal cycles may be used if the total pulse duration, or length, is of the same order as the required resolution. These types of pulses will be termed "short duration interfering" pulses.
Patent application Ser. No. 07/106,577, which is a continuation in part of patent application Ser. No. 06/858,696 further describes the Ellipsoidal Backprojection image reconstruction technique which is used for image reconstruction in patent application Ser. No. 06/858,577.
Ellipsoidal Backprojection is a method for the active imaging of a three dimensional volume using a single transmitted pulse or greatly reduced number of transmitted pulses and is discussed in detail in the previously mentioned patents and patent applications. Referring to FIG. 1, a short pulse of energy is transmitted which radiates outward, as an expanding sphere, through a wide solid angle. Echoes are received by a sparse array of receiver elements and, typically, then digitized into echo samples. These samples are then backprojected over ellipsoids through the image by one means or another. The results constitute, basically, the reconstructed image, although additional processing steps may be implemented.
Ellipsoidal Backprojection is a linear image reconstruction method, although the point spread function varies with location of the reconstruction point. The point spread function is the image of a point object as reconstructed by the imaging system. In a linear imaging system, the final, reconstructed image is, essentially, the convolution of the point spread function with the original object to be imaged. This is well known and is described in: Introduction to Fourier Optics--Goodman; Linear Systems, Fourier Transforms, and Optics--Gaskill; or The Fourier Transform and its Application to Optics--Duffiuex.
The point spread function determines the imaging capabilities of a linear imaging system. Ellipsoidal Backprojection alone yields an adequate point spread function, however, a particular type of linear filter may be applied to the echo time histories, before backprojection, which greatly improves the resolution while substantially reducing the sidelobe levels. The resulting imaging system is still linear.